We consider an initial and Dirichlet boundary value problem for
a fourth-order linear stochastic parabolic equation, in one space
dimension, forced by an additive space-time white noise.
Discretizing the space-time white noise a modelling error is
introduced and a regularized fourth-order linear stochastic
parabolic problem is obtained. Fully-discrete approximations to the solution of the regularized
problem are constructed by using, for discretization in space, a
Galerkin finite element method based on C0 or C1
piecewise polynomials, and, for time-stepping, the Backward Euler
method.
We derive strong a priori estimates for the modelling error and for
the approximation error to the solution of the regularized
problem.

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